A piston pump for which a control arrangement of the kind referred to above is suitable is disclosed, for example, in German published patent application DE-OS No. 34 10 911. Such piston pumps are utilized typically as contractor's pumps for withdrawing dirty water from excavations and the like. This entails especially the pumping of gas-free liquids. When the ground water table drops, a negative pressure can occur in the intake pipe of such contractor's pumps, such negative pressure acting as a pulling load on the pump piston after the latter has reversed the direction of its travel. Moreover, a breakdown of the liquid column in the suction chamber of the pump can result in cavitation. Such compressive loads on the pump piston can lead to undesirable accelerations of the piston after the latter has reversed the friction of its travel, thus causing damage to seals as a result of the frictional heat caused by the acceleration. Contractor's pumps must be self-priming, that is to say they must initially be able to pump air. Next, the pump must also be able to pump mixtures of air and water, with the air contained in the water constituting a compressible substance which, having been compressed by the pump, in turn constitutes an additional load acting upon the pump's piston rod.